Natural convection heat transfer of nanofluids along a vertical plate embedded in porous medium
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NANO EXPRESS
Open Access
Natural convection heat transfer of nanofluids along a vertical plate embedded in porous medium Ziya Uddin1,2* and Souad Harmand1,2
Abstract The unsteady natural convection heat transfer of nanofluid along a vertical plate embedded in porous medium is investigated. The Darcy-Forchheimer model is used to formulate the problem. Thermal conductivity and viscosity models based on a wide range of experimental data of nanofluids and incorporating the velocity-slip effect of the nanoparticle with respect to the base fluid, i.e., Brownian diffusion is used. The effective thermal conductivity of nanofluid in porous media is calculated using copper powder as porous media. The nonlinear governing equations are solved using an unconditionally stable implicit finite difference scheme. In this study, six different types of nanofluids have been compared with respect to the heat transfer enhancement, and the effects of particle concentration, particle size, temperature of the plate, and porosity of the medium on the heat transfer enhancement and skin friction coefficient have been studied in detail. It is found that heat transfer rate increases with the increase in particle concentration up to an optimal level, but on the further increase in particle concentration, the heat transfer rate decreases. For a particular value of particle concentration, small-sized particles enhance the heat transfer rates. On the other hand, skin friction coefficients always increase with the increase in particle concentration and decrease in nanoparticle size. Keywords: Nanofluid, Convection, Porous medium, Implicit FDM, Numerical solution
Background Natural convection heat transfer in porous media is an important phenomenon in engineering systems due to its wide applications such as cooling of electronics components, heat exchangers, drying processes, building insulations, and geothermal and oil recovery. Due to high surface area, fluid mixing qualities, high thermal conductivity, and wide industrial applications, natural convection through porous media has gained considerable attention of various researchers in the past few decades. Cheng and Minkowycz [1] studied free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. They used the boundary layer approximations and found the similarity solution for the problem. Evans and Plumb [2] investigated natural convection about a vertical plate embedded in a medium composed of glass beads with * Correspondence: [email protected] 1 Université de Lille Nord de France, Lille F-59000, France 2 TEMPO/DF2T, UVHC, Valenciennes F-59313, France
diameters ranging from 0.85 to 1.68 mm. Their experimental data was in good agreement with the theory. Cheng [3] and Hsu [4] investigated the Darcian free convection flow about a semi-infinite vertical plate. They used the higher-order approximation theory and confirmed the results of Evans and Plumb [2]. Kim and Vafai [5] analyzed the natural convection about a vertical plate emb
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